"Political ambitions" refers to a person's desire or goals to hold a position of power or influence in the field of politics, with the aim of shaping and making decisions that affect society and its governance. Full definition
The mayor also faced a number of questions about his national political ambitions and whether he'll try to raise money to boost them. (ny1.com)
What I find most troubling is the question of whether this vital issue is being used for political ambition (not the issue itself nor bringing it to the fore). (thelodownny.com)